Phi: The Golden Ratio

Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.

- Mario Livio, The Golden Ratio: The Story of Phi, The World's Most Astonishing Number

The following 50,000 decimal place number for Phi was calculated by the University of Arizona computer science department on March 27, 1996.

First published 2006-12-31. The last major review or update of this information was on 2011-04-07. Your feedback using the form below helps us correct errors and omissions on this page.

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